ISSN 2542–0380
Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал | Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics

© Институт механики
им. Р.Р. Мавлютова

Яндекс.Метрика web site traffic statistics

Ilyasov A.M., Kireev V.N., Urmancheev S.F., Akhatov I.Sh. Mathematical modeling of steady stratified flows Proceedings of the Institute of Mechanics of Ufa Branch of RAS. 3 (2003). 195–207.
2003. Vol. 3. Issue 1, Pp. 195–207
DOI: 10.21662/uim2003.1.014
Mathematical modeling of steady stratified flows
Ilyasov A.M., Kireev V.N., Urmancheev S.F., Akhatov I.Sh.
Institute of Mechanics, Ufa
Bashkir state university, Ufa


The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters.

A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method.

The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results.

Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.


hydraulic approach,
hydraulic resistance,
two-fluid model,
finite-difference methods,
laminar flow,
interphase boundary,
VOF method,
stratified flow,
numerical simulation